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Event-Triggered Regulation of Mixed-Autonomy Traffic Under Varying Traffic Conditions

Yihuai Zhang, Huan Yu

TL;DR

This work tackles congestion in mixed-autonomy freeway traffic, modeling HVs and AVs with a $4\times4$ extended ARZ PDE system and boundary ramp metering. It develops an event-triggered control framework grounded in backstepping to achieve stabilization with far fewer updates, and it extends to an observer-based ETC to accommodate limited sensing while proving exponential convergence in the $L^2$ sense and avoiding Zeno behavior. A dynamic triggering law and minimal dwell-time analysis underpin the theoretical guarantees, complemented by extensive simulations across AV penetration rates, spacing policies, and demand levels. Results show ramp-metering ETC can stabilize mixed flows, reduce driver distraction, and leverage AV presence to mitigate congestion and lower resource use.

Abstract

Modeling and congestion mitigation of mixed-autonomy traffic systems consisting of human-driven vehicles (HVs) and autonomous vehicles (AVs) have become increasingly critical with the rapid development of autonomous driving technology. This paper develops an event-triggered control (ETC) framework for mitigating congestion in such systems, which are modeled using an extended Aw-Rascle-Zhang (ARZ) formulation consisting of coupled 4 x 4 hyperbolic partial differential equations (PDEs). Ramp metering is employed as the boundary actuation mechanism. To reduce computational and communication burdens while avoiding excessive ramp signal changes, we design the ETC strategy based on the backstepping method, together with an observer-based ETC formulation for practical implementation under limited sensing. Rigorous Lyapunov analysis ensures exponential convergence and avoidance of Zeno behavior. Extensive simulations validate the proposed approach under diverse traffic scenarios, including varying AV penetration rates, different spacing policies, multiple demand levels, and non-recurrent congestion patterns. Results show that ETC not only stabilizes mixed traffic flows but also significantly reduces control updates, improving driver comfort, and roadway safety. Higher AV penetration rates lead to longer release time and fewer triggering events, indicating the positive impact of AVs in mitigating traffic congestion while reducing computational resource usage. Compared to continuous backstepping controllers, the proposed ETC achieves near-equivalent stabilization performance with far fewer controller updates, resulting in longer signal release time that reduces driver distraction, which demonstrates great potential for ETC applications in traffic management.

Event-Triggered Regulation of Mixed-Autonomy Traffic Under Varying Traffic Conditions

TL;DR

This work tackles congestion in mixed-autonomy freeway traffic, modeling HVs and AVs with a extended ARZ PDE system and boundary ramp metering. It develops an event-triggered control framework grounded in backstepping to achieve stabilization with far fewer updates, and it extends to an observer-based ETC to accommodate limited sensing while proving exponential convergence in the sense and avoiding Zeno behavior. A dynamic triggering law and minimal dwell-time analysis underpin the theoretical guarantees, complemented by extensive simulations across AV penetration rates, spacing policies, and demand levels. Results show ramp-metering ETC can stabilize mixed flows, reduce driver distraction, and leverage AV presence to mitigate congestion and lower resource use.

Abstract

Modeling and congestion mitigation of mixed-autonomy traffic systems consisting of human-driven vehicles (HVs) and autonomous vehicles (AVs) have become increasingly critical with the rapid development of autonomous driving technology. This paper develops an event-triggered control (ETC) framework for mitigating congestion in such systems, which are modeled using an extended Aw-Rascle-Zhang (ARZ) formulation consisting of coupled 4 x 4 hyperbolic partial differential equations (PDEs). Ramp metering is employed as the boundary actuation mechanism. To reduce computational and communication burdens while avoiding excessive ramp signal changes, we design the ETC strategy based on the backstepping method, together with an observer-based ETC formulation for practical implementation under limited sensing. Rigorous Lyapunov analysis ensures exponential convergence and avoidance of Zeno behavior. Extensive simulations validate the proposed approach under diverse traffic scenarios, including varying AV penetration rates, different spacing policies, multiple demand levels, and non-recurrent congestion patterns. Results show that ETC not only stabilizes mixed traffic flows but also significantly reduces control updates, improving driver comfort, and roadway safety. Higher AV penetration rates lead to longer release time and fewer triggering events, indicating the positive impact of AVs in mitigating traffic congestion while reducing computational resource usage. Compared to continuous backstepping controllers, the proposed ETC achieves near-equivalent stabilization performance with far fewer controller updates, resulting in longer signal release time that reduces driver distraction, which demonstrates great potential for ETC applications in traffic management.

Paper Structure

This paper contains 24 sections, 5 theorems, 67 equations, 18 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Mixed-autonomy traffic modeling and control
  3. Event-triggered control
  4. Contribution
  5. Mixed-Autonomy Traffic PDE Model
  6. Different spacing policies and fundamental diagram
  7. Free/congested traffic analysis
  8. Boundary Controller Design
  9. Backstepping transformation
  10. Inverse Transformation
  11. Event-triggered Controller Design
  12. Dynamic triggering condition
  13. Avoidance of Zeno phenomenon
  14. Observer-based event-triggered controller
  15. Experiments
  16. ...and 9 more sections

Key Result

Theorem 1

Consider the plant clpsys1-clpsys4 with the backstepping control law control_law. For given initial conditions $(\mathbf{w}^+_0,\mathbf{w}^-_0)\in L^2((0,L),\mathbb{R}^4)$, the equilibrium $\mathbf{w}\equiv 0$ is finite-time stable in the $L^2$ sense and the equilibrium is reached in finite time $t_

Figures (18)

  • Figure 1: The mixed-autonomy traffic system with different spacing policy. $s_{\rm h}$ denotes the spacing of HVs, $s_{\rm a}$ represents the spacing of AVs. The impact area is calculated by Eq. \ref{['impactHV']} and \ref{['impactAV']}.
  • Figure 2: The fundamental diagram of HVs and AVs using area occupancy(AO)
  • Figure 3: The fundamental diagram of HVs and AVs using original densities
  • Figure 4: The free and congestion region determined by $\lambda_4$. $\lambda_4<0$ denotes the congested region while the other denotes the free region of the mixed-autonomy traffic system.
  • Figure 5: The open-loop traffic density and speed of mixed-autonomy traffic system. Traffic states oscillate in the simulation period.
  • ...and 13 more figures

Theorems & Definitions (14)

  • Remark 1
  • Theorem 1: burkhardt2021stopburkhardt_suppression_2020
  • Definition 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • ...and 4 more